Introduction to modern algebra Book

Preface

Introduction
1. Some Fundamental Concepts
1.1 Sets
1.2 Mappings
1.3 Equifalence Relations
1.4 Operations
2.Rings
2.1 Formal Properties of the Integers
2.2 Definition of a Ring
2.3 Examples of Rings
2.4 Some Properties of Addition and Multiplication
2.5 General Sums and Products
2.6 Integers Modulo n
2.7 Homomorphisms and Isomorphisms
3. Integral Domains and Fields
3.1 Definition of Integral Domain
3.2 Ordered Integral Domains
3.3 Well-Ordering and Mathematical Induction
3.4 A Characterization of the Ring of Integers
3.5 Fields
3.6 Field of Quotients
3.7 Properties of the Field of Rational Numbers
3.8 The Field of Real Numbers
3.9 Properties of the Field of Real Numbers
3.10 The Field of Complex Numbers
3.11 Geometric Representation and Trigonometric Form
3.12 The nth Roots of a Complex Number
4. Factorization
4.1 Divisors and the Division Algorithm for Z
4.2 Greatest Common Divisors in Z
4.3 The Fundamental Theorem in Z
(and more...)